- - - - Monday, Oct 30, 2023 - - - -

Rutgers Logic Seminar

Monday, Oct 30th, 3:30pm, Rutgers University, Hill 705

Filippo Calderoni, Rutgers

Condensation and solvable left-orderable groups

Logic and Metaphysics Workshop

Date: Monday, Oct 30, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Brad Armour-Garb (SUNY Albany).

Title: An approach to property-talk for property nominalists

Abstract: Properties, understood as immanent universals that are repeatable entities which distinct objects can each have at the same time and in different places, are weird, so weird, in fact, that if we could do without them, we probably should do so. An alternative to an approach that sanctions properties might suggest a deflationary view of property-talk according to which the raison d’être of our use of ‘property’ is that it serves a quasi-logical function that is akin to what alethic deflationists claim about truth-talk. Deflationists about property-talk normally subscribe to a form of property nominalism, which rejects the sort of property realism that takes properties to be immanent universals. In this talk, after highlighting some of the weirdness of, or worries for, property realism and explaining why certain forms of property nominalism should not be abided, I highlight the expressive role of property-talk and go on to explain how property-talk performs its roles by introducing what I call “adjectival predicate-variable deflationism” (“APVD”). As I will show, by incorporating APVD into a version of what I have called a “semantic-pretense involving fictionalism” (“SPIF”), we capture the full range of property-talk instances without compromising property nominalism. Time permitting, I will also highlight a virtue of my view, which another form of property nominalism cannot accommodate. If property nominalism is correct, then we should endorse the SPIF account of property-talk that I will develop in this talk.

Note: This is joint work with James A. Woodbridge.

- - - - Tuesday, Oct 31, 2023 - - - -

- - - - Wednesday, Nov 1, 2023 - - - -

- - - - Thursday, Nov 2, 2023 - - - -

- - - - Friday, Nov 3, 2023 - - - -

Model Theory Seminar

Friday, Nov 3, 12:30-2:00pm NY time, Room 5383

Alfred Dolich CUNY

Definable sets in rank two expansions of ordered groups

I will discuss work on burden 2 or dp-rank 2 expansions of theories of densely ordered Abelian groups. Such theories allow for some variety in the topological properties of definable subsets in their models and I'll discuss how diverse the collection of definable subsets in a model may be. For example, is it possible to simultaneously define an infinite discrete set and a dense co-dense subset? Answers to such questions often hinge on whether one is working in the inp-rank or dp-rank case (i.e. whether one assumes NIP or not). I will provide definitions in the talk of all the relevant notions. This is joint work with John Goodrick.

Logic Workshop

CUNY Graduate Center

Friday Nov 3, 2:00pm-3:30pm, Room 6417

Karel Hrbacek, CUNY

Nonstandard methods without the Axiom of Choice

Model-theoretic frameworks for nonstandard methods entail the existence of nonprincipal ultrafilters over N, a strong version of the Axiom of Choice (AC). While AC is instrumental in many abstract areas of mathematics, such as general topology or functional analysis, its use in infinitesimal calculus or number theory should not be necessary.

Mikhail Katz and I have formulated a set theory SPOT in the language that has, in addition to membership, a unary predicate “is standard.” In addition to ZF, the theory has three simple axioms, Transfer, Nontriviality and Standard Part, that reflect the insights of Leibniz. It is a subtheory of the nonstandard set theories IST and HST, but unlike them, it is a conservative extension of ZF. Arguments carried out in SPOT thus do not depend on any form of AC. Infinitesimal calculus can be developed in SPOT as far as the global version of Peano's Theorem (the usual proofs of which use ADC, the Axiom of Dependent Choice). The existence of upper Banach densities can be proved in SPOT.

The conservativity of SPOT over ZF is established by a construction that combines the methods of forcing developed by Ali Enayat for second-order arithmetic and Mitchell Spector for set theory with large cardinals.

A stronger theory SCOT is a conservative extension of ZF+ADC. It is suitable for handling such features as an infinitesimal approach to the Lebesgue measure.

I will also formulate an extension of SPOT to a theory with multiple levels of standardness SPOTS, in which Renling Jin's recent groundbreaking proof of Szemeredi's Theorem can be carried out. While it is an open question whether SPOTS is conservative over ZF, SPOTS + DC (Dependent Choice for relations definable in it) is a conservative extension of ZF + ADC.

Reference: KH and M. G. Katz, Infinitesimal analysis without the Axiom of Choice, Ann. Pure Applied Logic 172, 6 (2021).

https://doi.org/10.1016/j.apal.2021.102959,

https://arxiv.org/abs/2009.04980

Next Week in Logic at CUNY:

- - - - Monday, Nov 6, 2023 - - - -

Logic and Metaphysics Workshop

Date: Monday, Nov 6, 4.15-6.15pm (NY time)

Room: Graduate Center Room 4419

Alex Citkin (Metropolitan Telecommunications).

Title: On logics of acceptance and rejection

Abstract: In his book *Formalization of Logic*, Carnap suggested the following process of refutation: for any set of formulas Γ and any formula *α,* if Γ ⊢ *α *and *α *is rejected, reject Γ. Thus, in contrast to the Łukasiewicz’s approach to refutation, the predicate of rejection is defined on sets of formulas rather than just formulas. In addition to a predicate of rejection, we introduce a predicate of acceptance which is also defined on sets of formulas, and this leads us to constructing two-layered logical systems, the ground layer of which is a conventional deductive system (providing us with means for derivation), and the top layer having predicates of acceptance and rejection. In the case when the set of accepted formulas coincides with the set of theorems of the underlying logic and the set of rejected formulas coincides with the sets of non-theorems, we obtain a conventional deductive system. The predicate of acceptance can be non-adjunctive, and this allows us to use such systems as an alternative approach to defining Jaśkowski style discursive logics.

- - - - Tuesday, Nov 7, 2023 - - - -

Models of Peano Arithmetic (MOPA)

Tuesday, Nov 7, 1:00pm

Virtual (email Victoria Gitman

vgitman@gmail.com for meeting id)

Stefan Hetzl, Vienna University of Technology

- - - - Wednesday, Nov 8, 2023 - - - -

The New York City Category Theory Seminar

Department of Computer Science

Department of Mathematics

The Graduate Center of The City University of New York

URL:

http://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.htmlSpeaker: ** Larry Moss, Indiana University, Bloomington .**

Date and Time: ** Wednesday November 8, 2023, 7:00 - 8:30 PM. ZOOM TALK**

Title:** On Kripke, Vietoris, and Hausdorff Polynomial Functors.**

Abstract: The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor V on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from V, the identity and constant functors by forming products, coproducts and compositions. These functors are known to have terminal coalgebras and we deduce that they also have initial algebras. We present an analogous class of endofunctors on the category of extended metric spaces, using in lieu of V the Hausdorff functor H. We prove that the ensuing Hausdorff polynomial functors have terminal coalgebras and initial algebras. Whereas the canonical constructions of terminal coalgebras for Vietoris polynomial functors takes omega steps, one needs \omega + \omega steps in general for Hausdorff ones. We also give a new proof that the closed set functor on metric spaces has no fixed points.

- - - - Thursday, Nov 9, 2023 - - - -

- - - - Friday, Nov 10, 2023 - - - -

Model Theory Seminar

Friday, Nov 10, 12:30-2:00pm NY time, Room 5383

Alexander Van Abel Wesleyan University

Logic Workshop

CUNY Graduate Center

Friday Nov 10, 2:00pm-3:30pm, Room 6417

**Victoria Gitman**, CUNY

**Upward Löwenheim Skolem numbers for abstract logics**

Galeotti, Khomskii and Väänänen recently introduced the notion of the upward Löwenheim Skolem (ULS) number for an abstract logic. A cardinal κ is the upward Lowenheim Skolem number for a logic L if it is the least cardinal with the property that whenever M is a model of size at least κ satisfying a sentence φ in L, then there are arbitrarily large models N satisfying φ and having M as a substructure (not necessarily elementary). If we remove the requirement that M has to be a substructure of N, we get the classic notion of a Hanf number. While ZFC proves that every logic has a Hanf number, having a ULS number often turns out to have large cardinal strength. In a joint work with Jonathan Osinski, we study the ULS numbers for several classical logics. We introduce a strengthening of the ULS number, the strong upward Löwenheim Skolem number SULS which strengthens the requirement that M is a substructure to full elementarity in the logic L. It is easy to see that both the ULS and the SULS number for a logic L are bounded by the least strong compactness cardinal for L, if it exists.