28 citations · 90 across the 17 of their papers we have counts for
18 papers
Three surprising instances of dividing
Gabriel Conant, Alex Kruckman
We give three counterexamples to the folklore claim that in an arbitrary theory, if a complete type over a set does not divide over , then no extension of …
A New Kim's Lemma
Alex Kruckman, Nicholas Ramsey
Kim's Lemma is a key ingredient in the theory of forking independence in simple theories. It asserts that if a formula divides, then it divides along every Morley sequence in type…
Interpolative fusions II: Preservation results
Alex Kruckman, Minh Chieu Tran, Erik Walsberg
We study interpolative fusion, a method of combining theories and in distinct languages in a "generic" way over a common reduct , to obtain a theory .…
Invariant measures in simple and in small theories
Artem Chernikov, Ehud Hrushovski, Alex Kruckman +4
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measur…
The almost sure theory of finite metric spaces
Isaac Goldbring, Bradd Hart, Alex Kruckman
We establish an approximate zero-one law for sentences of continuous logic over finite metric spaces of diameter at most . More precisely, we axiomatize a complete metric theory…
Examples of weak amalgamation classes
Adam Krawczyk, Alex Kruckman, Wiesław Kubiś +1
We present several examples of hereditary classes of finite structures satisfying the joint embedding property and the weak amalgamation property, but failing the cofinal amalgamat…
Interpolative Fusions I
Alex Kruckman, Minh Chieu Tran, Erik Walsberg
We define the interpolative fusion of a family of first-order theories over a common reduct , a notion that generalizes many examples of random…
Higher dimensional obstructions for star reductions
Alex Kruckman, Aristotelis Panagiotopoulos
A -reduction between two equivalence relations is a Baire measurable reduction which preserves generic notions, i.e., preimages of meager sets are meager. We show that a -red…
Exploring the Landscape of Relational Syllogistic Logics
Alex Kruckman, Lawrence S. Moss
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decida…
Properly ergodic structures
Nathanael Ackerman, Cameron Freer, Alex Kruckman +1
We consider ergodic -invariant probability measures on the space of -structures with domain (for a countable relational language), and…
Independence in generic incidence structures
Gabriel Conant, Alex Kruckman
We study the theory of existentially closed incidence structures omitting the complete incidence structure , which can also be viewed as existentially closed $K_…
Tameness in least fixed-point logic and McColm's conjecture
Siddharth Bhaskar, Alex Kruckman
We investigate four model-theoretic tameness properties in the context of least fixed-point logic over a family of finite structures. We find that each of these properties depends…
Generic expansion and Skolemization in NSOP theories
Alex Kruckman, Nicholas Ramsey
We study expansions of NSOP theories that preserve NSOP. We prove that if is a model complete NSOP theory eliminating the quantifier , then the ge…
Disjoint -amalgamation and pseudofinite countably categorical theories
Alex Kruckman
Disjoint -amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this paper,…
Actions arising from intersection and union
Alex Kruckman, Lawrence Valby
An action is a pair of sets, and , and a function . Rothschild and Yalcin gave a simple axiomatic characterization of those actions arising from set…
The Ax-Kochen Theorem: an application of model theory to algebra
Alex Kruckman
The Ax-Kochen Theorem is a purely algebraic statement about the zeros of homogeneous polynomials over the p-adic numbers, but it was originally proved using techniques from mathema…
A Myhill-Nerode theorem for automata with advice
Alex Kruckman, Sasha Rubin, John Sheridan +1
An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to character…
Chains of distributions, hierarchical Bayesian models and Benford's Law
Dennis Jang, Jung Uk Kang, Alex Kruckman +2
Kossovsky recently conjectured that the distribution of leading digits of a chain of probability distributions converges to Benford's law as the length of the chain grows. We prove…