The topological pigeonhole principle for ordinals

Given a cardinal $\kappa$ and a sequence $\left(\alpha_i\right)_{i\in\kappa}$ of ordinals, we determine the least ordinal $\beta$ (when one exists) such that the topological partition relation $$\beta\rightarrow\left(top\,\alpha_i\right)^1_{i\in\kappa}$$ holds, including an independence result for one class of cases. Here the prefix "$top$" means that the homogeneous set must have the correct topology rather than the correct order type. The answer is linked to the non-topological pigeonhole principle of Milner and Rado.Comment: 24 page

Cultural Resources Survey for the Proposed Warehouse Center Drive Project located in Harris County, Texas

In October 2017, Gray & Pape, Inc., of Houston, Texas, performed an intensive pedestrian cultural resources survey of approximately 13.8 hectares (34 acres) of land proposed for development in northeast Harris County, Texas. The Lead Federal Agency for this project has been identified as the United States Army Corps of Engineers, Galveston District. The goals of the survey were to establish whether previously unidentified buried archaeological resources were located within or immediately adjacent to the project’s Area of Potential Effects and if so to provide management recommendations for such resources. The survey was undertaken in accordance with requirements set forth by Section 106 of the National Historic Preservation Act, specifically requirements set forth by 36 CFR 800. The procedures to be followed by the United States Army Corps of Engineers to fulfill the requirements set forth in the National Historic Preservation Act, other applicable historic preservation laws, and Presidential directives as they relate to the regulatory program of the United States Army Corps of Engineers (33 CFR Parts 320-334) are articulated in the Regulatory Program of the United States Army Corps of Engineers, Part 325 - Processing of Department of the Army Permits, Appendix C - Procedures for the Protection of Historic Properties. All fieldwork and reporting activities were completed with reference to State laws and guidelines (the Antiquities Code of Texas). Survey and site identification followed Texas Antiquities Code standards. Fieldwork took place between October 13 and 17, 2017, and required 48 person hours to complete. Field investigation consisted of intensive pedestrian surface inspection, subsurface shovel testing, photographic documentation, and mapping. A total of 22 shovel tests were excavated. No prehistoric or historic artifacts or cultural features were observed. No new or previously recorded archaeological sites were located within the project boundary. Based on the results of the survey, Gray & Pape, Inc. recommends that no further cultural resources work be required and that the project be cleared to proceed as currently planned

Cultural Resource Investigations for the Praxair Phillips 66 H2 Pipeline in Brazoria County, Texas

Gray & Pape, Inc. was contracted to conduct a cultural resources survey for a proposed pipeline project. The project is a 14-inch pipeline from Praxair Freeport Plant to the Phillips 66 Clemens Storage Cavern located near Freeport, Texas. The project route measures approximately 28.0 kilometers (17.4 miles). The project’s Area of Potential Effect is the entire alignment route within a survey corridor of 91.4 meters (300 feet). This amounts to approximately 252 hectares (622 acres). Subsequent workspace revisions resulted in an additional 25.7 hectares (63.4 acres) or 2.6 kilometers (1.6 miles) of workspace, documented in Appendix C of this final report. The pipeline will be collocated with several existing pipelines in a well-maintained corridor for the entire length. The Project is part of a Nationwide 12 permit for which the Lead Federal Agency is the United States Army Corps of Engineers, Galveston District. The procedures to be followed by the United States Army Corps of Engineers to fulfill the requirements set forth in the National Historic Preservation Act, other applicable historic preservation laws, and Presidential directives as they relate to the regulatory program of the United States Army Corps of Engineers (33 CFR Parts 320-334) are articulated in the Regulatory Program of the United States Army Corps of Engineers, Part 325 -Processing of Department of the Army Permits, Appendix C -Procedures for the Protection of Historic Properties. Approximately 3.6 kilometers (2.25 miles) of the project length is located within property owned by the Texas Department of Criminal Justice, Clemens Prison Unit, which necessitated the procurement of a permit subject to the Antiquities Code of Texas. Permit Number 8666 was assigned to the project on December 4, 2018. As required under the provisions of Texas Antiquities Code Permit, all project records are housed at the Center for Archaeological Studies at Texas State University, San Marcos, Texas. The goals of this study were to assist the client, the Texas Historical Commission, and other relevant agencies in determining whether intact cultural resources were present within areas planned for construction, and if so to provide management recommendations for these resources. All work conducted by Gray & Pape, Inc. followed accepted guidelines and standards set forth by the Texas Historical Commission and the Council of Texas Archeologists. Prior to field investigation, site file research was used to develop a cultural context for the study. This research resulted in a listing of all archaeological sites and National Register properties within 1.6 kilometers (1 mile) of the project area, as well as a discussion of archaeological potential within the tract. Previous surveys conducted by HRA Gray & Pape, LLC and other firms overlap approximately 6.1 kilometers (3.8 miles) / 55.4 hectares (137 acres) of the current project’s corridor. These surveys were undertaken from between 2012 to 2013. These areas along with an additional 2.8 kilometers (2 miles) / 28.9 hectares (71.3 acres) of highly disturbed pipeline corridor were subjected to visual reconnaissance survey only. Another 3.0 kilometers (1.9 miles) / 27.5 hectares (68 acres) of the project is located within highly industrial areas of DOW property and was subjected to desktop assessment and determined to be of low potential for containing intact cultural materials. No further work is recommended for these areas. No new cultural resources were discovered during the survey. Gray & Pape, Inc. recommends no survey within these portions due to the highly disturbed conditions. Intensive pedestrian survey was completed on those portions of the current project that fall outside of the previous survey coverage or that have potential to impact previously unidentified sites. This amounts to 15.6 kilometers (9.7 miles) / 140 hectares (346 acres). As a result of survey efforts, one previously unrecorded archaeological site was identified during survey efforts. As currently mapped, the site is overlapped by an existing pipeline corridor and does not retain integrity within the project right-of-way. Gray & Pape, Inc. recommends that no further investigation be necessary within the surveyed portions of the project

Cultural Resources Survey for the Proposed Knight Road Expansion, Fort Bend County, Texas

In October 2017, Gray & Pape, Inc., of Houston, Texas, conducted an intensive pedestrian cultural resources survey on property subsuming a total of approximately 8.3 hectares (20.4 acres) proposed for the extension and expansion of Knight Road in Fort Bend County, Texas. This area is defined as the Area of Potential Effects. Because the project involves the City of Missouri City, a political subdivision of the State of Texas, the project was assigned Antiquities Code Permit number 8189 by the Texas Historical Commission on October 5, 2017. The United States Army Corps of Engineers, Galveston District has been identified as the Lead Agency for this project. The goals of the survey were to establish whether previously unidentified buried archaeological resources were located within or immediately adjacent to the project’s Area of Potential Effects and if so to provide management recommendations for such resources. The survey was undertaken in accordance with requirements set forth by Section 106 of the National Historic Preservation Act, specifically requirements set forth by 36 CFR 800. The procedures to be followed by the United States Army Corps of Engineers to fulfill the requirements set forth in the National Historic Preservation Act, other applicable historic preservation laws, and Presidential directives as they relate to the regulatory program of the United States Army Corps of Engineers (33 CFR Parts 320-334) are articulated in the Regulatory Program of the United States Army Corps of Engineers, Part 325 - Processing of Department of the Army Permits, Appendix C - Procedures for the Protection of Historic Properties. All fieldwork and reporting activities were completed with reference to State laws and guidelines (the Antiquities Code of Texas). Survey and site identification followed Texas Antiquities Code standards. All records for this project are curated at the Center for Archaeological Studies at Texas State University in San Marcos, Texas. Fieldwork took place between October 6 and 10, 2017, and required 48 person hours to complete. Field investigation consisted of intensive pedestrian surface inspection, subsurface shovel testing, photographic documentation, and mapping. A total of 28 shovel tests were excavated, none of which were positive for buried cultural materials. Another nine attempted shovel tests were unexcavated due to inundation, buried utilities, and disturbances such as drainage ditches. Overall, the project largely exhibited either disturbance by existing development and the channelization of Oyster Creek, or inundation due to the low and wet landscape of the area. Two surface finds of cultural materials were identified as a result of survey, these being a pile of discarded modern brick and mortar and a scatter of corrugated metal siding. These finds may have resulted from the previous use of the property as farmstead or ranch or from previous road and culvert construction. Due to the modern nature of the materials, a trinomial was not requested for the finds. Other isolated modern materials were also identified within and near the project likely as a result of localized flooding and trash dumping because of the secluded nature of the location. Based on the results of the survey, Gray & Pape, Inc. recommends that no further cultural resources work be required and that the project be cleared to proceed as currently planned

Cultural Resources Survey of 98 Acres for the Proposed Taylor Morrison Development Project, Fort Bend County, Texas

In November 2017, Gray & Pape, Inc. of Houston, Texas, conducted an intensive pedestrian cultural resources survey and deep testing on property subsuming a total of approximately 40 hectares (98 acres) proposed for development in Fort Bend County, Texas. No Texas Antiquities Permit was required as all survey work was completed on privately-owned property. The United States Army Corps of Engineers-Galveston District has been identified as the Lead Agency for this project. The goals of the survey were to establish whether previously unidentified buried archaeological resources were located within or immediately adjacent to the project’s Area of Potential Effects, which is defined as all 40 hectares (98 acres), and if so to provide management recommendations for such resources. The survey was undertaken in accordance with requirements set forth by Section 106 of the National Historic Preservation Act, specifically requirements set forth by 36 CFR 800. The procedures to be followed by the United States Army Corps of Engineers to fulfill the requirements set forth in the National Historic Preservation Act, other applicable historic preservation laws, and Presidential directives as they relate to the regulatory program of the United States Army Corps of Engineers (33 CFR Parts 320-334) are articulated in the Regulatory Program of the United States Army Corps of Engineers, Part 325 - Processing of Department of the Army Permits, Appendix C - Procedures for the Protection of Historic Properties. All fieldwork and reporting activities were completed with reference to State laws and guidelines (the Antiquities Code of Texas). Survey and site identification followed Texas Antiquities Code standards. Fieldwork took place between November 13 and November 22, and required 116-person hours to complete. Field investigations consisted of intensive pedestrian surface inspection, subsurface shovel testing, photographic documentation, mapping, and mechanical deep testing. A total of 59 shovel tests and six deep tests were excavated. Only one shovel test was positive for cultural materials. This test contained a porcelain insulator at a depth of 10 centimeters (4 inches) below surface. This isolated find was completely delineated with no additional materials found within a 20-meter (65-foot) radius. This isolate was located immediately adjacent to Snake Slough and could have washed into place during a flood event. Also, it was located near the intersection of two buried utilities and could have been deposited during their construction. This isolate is not recommended for further investigation and no state-issued trinomial was requested. No new buried significant cultural sites were encountered as a result of survey. Two historical above-ground resources were identified, which include a circa 1950s vernacular residence and the remains of an oil drilling platform. Neither resource is associated with significant events or persons, and are not likely to provide important information about the history of the oil industry in Fort Bend County, nor do they represent distinctive architectural design characteristics. Therefore, neither resource appears to meet the minimum requirements for inclusion in the National Register of Historic Places and no further work is recommended regarding them. The historic-age resources are not recommended as eligible for inclusion in the National Register of Historic Places. No negative impacts on archaeological sites or significant above-ground resources are anticipated as a result of project construction. Based on these findings, Gray & Pape, Inc. recommends that no further cultural resources work be required and that the project be cleared to proceed as currently planned

Archaeological Survey for the Lower Greens Bayou Trail Project, Segments GR02 and GR03, in Harris County, Texas

Over several mobilizations between April 2018 and January 2020, Gray & Pape, Inc., of Houston, Texas, conducted an intensive pedestrian cultural resources survey of two segments (Segments GR02 and GR03) of proposed trail development along Lower Greens Bayou in the City of Houston, Harris County, Texas. The project alignment measures approximately 10.8 kilometers (6.7 miles) in length and encompasses approximately 9.6 hectares (23.7 acres) of area. Another 0.6 kilometers (0.4 miles) or 0.6 hectares (1.4 acres) of project alignment was removed from consideration. In total, approximately 11.4 kilometers (7.1 miles) or 10.2 hectares (25.1 acres) was surveyed for the project. Because the proposed trail development occurs on publicly owned properties a Texas Antiquities Code Permit was required prior to survey. All work was completed under Texas Antiquities Permit #8328, which was assigned by the Texas Historical Commission on February 14, 2018. Fieldwork and reporting activities were performed according to procedures set forth by the Texas Historical Commission and the Council of Texas Archeologists. The goals of the survey were to establish whether or not previously unidentified archaeological resources were located within the project area, also defined as the project’s Area of Potential Effects, and whether the proposed development would affect any previously identified cultural resources. Prior to fieldwork, site file and background research was conducted, including a review of historic aerial and topographic maps in an attempt to locate any historic structures associated with the Area of Potential Effects. Site file review and background research indicated that there are no previously recorded sites within the project Area of Potential Effects. Fieldwork took place between April 10, 2018 and January 7, 2020 and consisted of a combination of pedestrian survey and shovel testing. Systematic shovel testing was performed along a single transect over both project segments resulting in 131 shovel tests being excavated, of which 11 were positive for cultural material. The survey revealed that large portions of both project segments have been heavily disturbed by development and flood events, however, three new archaeological sites, 41HR1234, 41HR1235, and 41HR1236, and one historic Isolate were identified as a result of survey. Site 41HR1234 was identified as a mid-twentieth century historic trash midden. Site 41HR1235 was identified as a Late Prehistoric ephemeral campsite. Site 41HR1236 was identified as a multicomponent prehistoric campsite and historic isolate. Diagnostic artifacts were observed at all three sites; however, it is the recommendation of Gray & Pape, Inc. that only Sites 41HR1235 and 41HR1236 are significant in the materials they contain and their potential to offer additional research potential. Direct impacts to both sites have been avoided by the project alignment as currently planned. While indirect impacts such as looting are a concern, the distance between the sites and the current alignment as well the density of woods surrounding them minimizes the danger as a result of the project. Eligibility testing is recommended for the sites if they cannot be avoided by future projects. Based on the results of this survey, Gray & Pape, Inc. recommends that the no further cultural resources work be required for the project as currently planned and that the project be cleared to proceed. As specified under the conditions of Texas Antiquities Code Permit #8328, all project associated records are curated with the Center of Archaeological Studies at Texas State University in San Marcos, Texas