On the inevitability of the consistency operator

We examine recursive monotonic functions on the Lindenbaum algebra of $\mathsf{EA}$. We prove that no such function sends every consistent $\varphi$ to a sentence with deductive strength strictly between $\varphi$ and $(\varphi\wedge\mathsf{Con}(\varphi))$. We generalize this result to iterates of consistency into the effective transfinite. We then prove that for any recursive monotonic function $f$, if there is an iterate of $\mathsf{Con}$ that bounds $f$ everywhere, then $f$ must be somewhere equal to an iterate of $\mathsf{Con}$

Vista: November 2, 2006

https://digital.sandiego.edu/vista/1541/thumbnail.jp

Lanthorn, vol. 41, no. 18, October 23, 2006

Lanthorn is Grand Valley State\u27s student newspaper, published from 1968 to the present

The Pan American (1989-02)

https://scholarworks.utrgv.edu/panamerican/1512/thumbnail.jp

Subatomic quantification (Volume 6)

The goal of this book is to explore the relationship between the cognitive notion of parthood and various grammatical devices expressing this concept in natural language. The monograph aims to investigate syntactic constructions and lexical categories, e.g., partitives, whole-adjectives, and multipliers, encoding different kinds of part-whole structures both in Slavic and non-Slavic languages. It is envisioned to inspire radical rethinking of the ontology of models accounting for nominal semantics. Specifically, it provides novel evidence for a mereotopological approach to meaning, i.e., a theory of wholes that captures not only parthood but also topological relations holding between parts. This evidence comes from the phenomenon of subatomic quantification, i.e., quantification over parts of referents of concrete count nouns