Compact posets and ramifiability of large cardinals

The main topics of this dissertation are devoted to the study of the partially ordered sets (posets, for short) by using the various consequences of the properties of their order structure in the study of topological spaces and large cardinals;In Section 2, we consider the existence of prime ideals as well as ultrafilters of posets, which play an essential role in the possibility of their embedding into posets in which the order relation is the set-theoretical inclusion. As an application of the results obtained in this Section, we introduce the notion of a subbase S of a poset P and derive some corresponding consequences;In Sections 3 and 4, a key Theorem and a novel technique of transfinite inductive proof are introduced for establishing directly the Tower and Complete Accumulation Point compactness of products of compact topological spaces;The Tower compactness of a topological space T is then proven to be equivalent to the A-inductivity of the poset of all proper open sets of T;In Section 5, coordinatewise construction of complete accumulation points of the countable infinite product of the real unit interval I is given. The results are used in establishing the solvability of infinite systems of linear equations each with at most a countable (finite or infinite) number of unknowns. The existence of a solution of such systems of linear equations over the reals is proved based on the compactness of the product topology and under the assumption that finite subsystem have uniformly bounded solutions;In Section 6, we introduce the concept of Receding sequences of ordinals which serves as the basic motivation for the partition properties of infinite cardinals which in turn lead to the notion of the ramifiablity of infinite cardinals;In Section 7, we consider the question of the existence of ramifiable cardinals and various properties which characterizes them;The existence of a C AC-ramifiable cardinal can be shown in ZFC + MA + ¬CH (where MA is the Martin\u27s axiom). This fact is proved in Section 7 in a rather simple way;In the absence of Martin\u27s axiom, however, a useful characterization of ramifiable cardinals can be derived. To this end in Section 7, we have introduced a special lexicographic order on a Hausdorff cardinal [alpha] which implies that [alpha] is ramifiable. On the other hand, the introduction of a special tree in Section 7 implies the converse provided [alpha] is strongly inaccessible

Generalized Domination.

This thesis develops the theory of the everywhere domination relation between functions from one infinite cardinal to another. When the domain of the functions is the cardinal of the continuum and the range is the set of natural numbers, we may restrict our attention to nicely definable functions from R to N. When we consider a class of such functions which contains all Baire class one functions, it becomes possible to encode information into these functions which can be decoded from any dominator. Specifically, we show that there is a generalized Galois-Tukey connection from the appropriate domination relation to a classical ordering studied in recursion theory. The proof techniques are developed to prove new implications regarding the distributivity of complete Boolean algebras. Next, we investigate a more technical relation relevant to the study of Borel equivalence relations on R with countable equivalence classes. We show than an analogous generalized Galois-Tukey connection exists between this relation and another ordering studied in recursion theory.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113539/1/danhath_1.pd

A framework for fuzzy topology with particular reference to sequentiality and countability

Pu and Liu's Q-theory is combined with Lowen's goodness criterion for fuzzy extensions to provide a framework for fuzzifying topology. This framework is used for the study of fuzzy countability properties and for the fuzzification of classical sequentiality. In extending classical notions to fuzzy theory care is taken to ensure that they are a special case of the emerging fuzzy concepts. An examination of convergence in the sense of Pu and Liu in special fuzzy topological spaces demonstrates the advantage of Chang's definition of fuzzy topology, which is therefore adopted. A new criterion (called excellence) for the suitability of the fuzzy extensions of classical topological properties is introduced. In addition to passing Lowen's goodness test, an excellent property is expected to behave, under fuzzy extensions of induction and coinduction, in a way resembling that of the original classical property under these constructions. Fuzzy second countability, quasi-first countability and fuzzy sequentiality are found to be excellent extensions of classical second countability, first countability and sequentiality respectively

Formal methods and digital systems validation for airborne systems

This report has been prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook. Its purpose is as follows: to outline the technical basis for formal methods in computer science; to explain the use of formal methods in the specification and verification of software and hardware requirements, designs, and implementations; to identify the benefits, weaknesses, and difficulties in applying these methods to digital systems used on board aircraft; and to suggest factors for consideration when formal methods are offered in support of certification. These latter factors assume the context for software development and assurance described in RTCA document DO-178B, 'Software Considerations in Airborne Systems and Equipment Certification,' Dec. 1992

Fourth NASA Langley Formal Methods Workshop

This publication consists of papers presented at NASA Langley Research Center's fourth workshop on the application of formal methods to the design and verification of life-critical systems. Topic considered include: Proving properties of accident; modeling and validating SAFER in VDM-SL; requirement analysis of real-time control systems using PVS; a tabular language for system design; automated deductive verification of parallel systems. Also included is a fundamental hardware design in PVS

Parameterized monads in linguistics

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.This dissertation follows the formal semantics approach to linguistics. It applies recent developments in computing theories to study theoretical linguistics in the area of the interaction between semantics and pragmatics and analyzes several natural language phenomena by parsing them in these theories. Specifically, this dissertation uses parameterized monads, a particular theoretical framework in category theory, as a dynamic semantic framework to reinterpret the compositional Discourse Representation Theory(cDRT), and to provide an analysis of donkey anaphora. Parameterized monads are also used in this dissertation to interpret information states as lists of presuppositions, and as dot types. Alternative interpretations for demonstratives and imperatives are produced, and the conventional implicature phenomenon in linguistics substantiated, using the framework. Interpreting donkey anaphora shows that parameterized monads is able to handle the sentential dependency. Therefore, this framework shows an expressive power equal to that of related frameworks such as the typed logical grammar and the dynamic predicate logic. Interpreting imperatives via parameterized monads also provides a compositional dynamic semantic analysis which is one of the main approaches to analysing imperatives

Denotational proof languages

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. [417]-421).by Konstantinos Arkoudas.Ph.D

Erramu Boneta. Festschrift for Rudolf P. G. de Rijk

Índice / Aurkibidea / Index / Sommaire:- Basque verbal morphology: redefining cases.- Periklesen hitzaldia (Hilen alde egina, Tuzididesek dakarrenez, II. Liburua, 35-46).- Arabako euskal testu zahar gehiago: Gamarra eta Luzuriaga, XVII. mendeko bi Arabarren lekukotza.- Hizketa formula ohikoak.- The functional structure of the Basque noun phrase.- Hitz elkarketa, argumentu egitura eta theta-rolak.- Amerindian tribal names in North America of possible Basque origin.- Napoleon-en kontrako Salvat Monho-ren zenbait bertso.- Tipología de las cláusulas relativas en las lenguas eslavas: el caso del checo.- Suppletion in the old Basque verb “to give”.- On the (im)possibility of prosodic focus marking in embedded context in Northern Bizkaian Basque.- Linking language-particular morphology with Universal Syntax.- Sobre variación lingüística.- Bare indefinites and distribitivity in Basque.- Komunztadura bikoitza eta lekualdatzea.- Euskal gramatika puntu batez: ahalaz eta ezinaz.- Los inicios de la vascología en Holanda.- Nota sobre las inscripciones ibéricas de Aubagnan.- On the position of the auxiliary in O’odham.- Laxotik errabotera.- Regarding Basque postpositions and related matters.- Artzibarko etxe-izenen inguruan.- Euskararen hasperena ikuspegi tipologiko eta diakronikotik.- Zenbatzeko sistemen inguruan.- Ergatiboa definitzen: lehenengo saioa gramatika sortzailean.- Etimologiae (proto)uasconicae LXV.- Egitura desberdina duten “antzeko” perpaus batzuen inguruan.- Aposizioa euskal hitz-elkarteetan.- De l’usage de l’étrangeté syntaxique.- Palatalization revisited: bustidura adieraz garriaren estatusaz ohar batzuk.- Focus of correction and remnant movement in Basque.- Aldi, bide, kide, erdi-arzizkiak?- On the relativisation of the “highest subject position”.- Konposizionalitatea.- Datibo-markazioa.- Hausnarketa batzuk euskararen egoeraren inguruan.- Infinitival complementation in Basque.- Euskal hiztegigintzaren historiarako oharrak.- Hiztegi Hirukoitza-ren kanpoko eta barruko historiaz

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Collected Papers (Neutrosophics and other topics), Volume XIV

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar