Related papers: Lovely pairs of models: the non first order case
In the first part we show a counterexample to a conjecture by Shelah regarding the existence of indiscernible sequences in dependent theories (up to the first inaccessible cardinal). In the second part we discuss generic pairs, and give an…
We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…
Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…
Soft uniform structures provide a way to speak about uniform closeness in a parameterized setting. Working over a fixed parameter set, we treat entourages as soft relations and introduce a notion of \emph{soft uniformity} whose axioms…
We introduce the notion of pseudo-algebraicity to study atomic models of first order theories (equivalently models of a complete sentence of $L_{\omega_1,\omega}$. Theorem: Let $T$ be any complete first-order theory in a countable language…
We prove that in a countable theory $T$ fully stable over a predicate $P$, any $\lam$-complete set $A$ has the $\lam$-existence property. This means that $A$ can be extended to a $\lam$-saturated model of $T$ without changing the $P$-part.…
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
We initiate a systematic study of the class of theories without the tree property of the second kind - NTP2. Most importantly, we show: the burden is "sub-multiplicative" in arbitrary theories (in particular, if a theory has TP2 then there…
In [Appl. Comput. Harmon. Anal., 46(3):664-673, 2019], O. Christensen and M. Hasannasab observed that assuming the existence of an operator $T$ sending $e_n$ to $e_{n+1}$ for all $n \in \mathbb{N}$ (where $(e_n)_{n \in \mathbb{N}}$ is a…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…
This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal structures, lovely pairs, fields with Mann groups, and…
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…
Does the class of linear orders have (one of the variants of) the so called (lambda, kappa)-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive, i.e. existence results. More generally,…