Zobrazeno 1 - 10
of 152
pro vyhledávání: '"LASKOWSKI, MICHAEL C."'
We prove various results around indiscernibles in monadically NIP theories. First, we provide several characterizations of monadic NIP in terms of indiscernibles, mirroring previous characterizations in terms of the behavior of finite satisfiability.
Externí odkaz:
http://arxiv.org/abs/2409.05223
We consider a large family of theories of equivalence relations, each with finitely many classes, and assuming the existence of an $\omega$-Erdos cardinal, we determine which of these theories are Borel complete. We develop machinery, including {\em
Externí odkaz:
http://arxiv.org/abs/2407.10370
Autor:
Braunfeld, Samuel1 (AUTHOR), Laskowski, Michael C.2 (AUTHOR)
Publikováno v:
Transactions of the American Mathematical Society, Series B. 10/4/2024, Vol. 11, p1226-1232. 7p.
We prove that for a countable, commutative ring $R$, the class of countable $R$-modules either has only countably many isomorphism types, or else it is Borel complete. The machinery gives a succinct proof of the Borel completeness of TFAB, the class
Externí odkaz:
http://arxiv.org/abs/2209.06898
We show that if a universal theory is not monadically NIP, then this is witnessed by a canonical configuration defined by an existential formula. As a consequence, we show that a hereditary class of relational structures is NIP (resp. stable) if and
Externí odkaz:
http://arxiv.org/abs/2209.05120
A proof of the Borel completeness of torsion free abelian groups is presented. This proof differs considerably from the approach of Paolini-Shelah.
Externí odkaz:
http://arxiv.org/abs/2202.07452
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), 4021-4026
We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a theory $T$ i
Externí odkaz:
http://arxiv.org/abs/2109.08943
We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence $\Phi$ as a class of structures in a related language. From this, we show that $\Phi$ has a Borel complete expansion if and only if $S_\in
Externí odkaz:
http://arxiv.org/abs/2109.06140
Publikováno v:
Model Th. 1 (2022) 15-30
Given a complete theory $T$ and a subset $Y \subseteq X^k$, we precisely determine the {\em worst case complexity}, with respect to further monadic expansions, of an expansion $(M,Y)$ by $Y$ of a model $M$ of $T$ with universe $X$. In particular, alt
Externí odkaz:
http://arxiv.org/abs/2107.10920
Publikováno v:
Trans. Amer. Math. Soc. Ser. B 8 (2021), 948-970
We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite sat
Externí odkaz:
http://arxiv.org/abs/2104.12989