# UCLA Logic Colloquium

The UCLA Logic Colloquium meets on alternate Fridays, at 4 p.m., in MS 6221.
The Logic Colloquium Chair is Artem Chernikov.
Here are links to the UCLA Logic Center, the Caltech-UCLA Logic Seminar, and the Philosophy Colloquium.

Talks are listed here in reverse chronological order.

# Logic Colloquium: 12/18/2018 - 12/18/2019

 Friday May 31 2019 16:00-16:50 (MS 6221) Joshua Wiscons (Sacramento State) TBA Abstract. TBAHide Friday Apr 19 2019 04:00-04:50 (MS 6221) Todor Tsankov (University Paris 7) TBA Abstract. TBAHide Friday Feb 22 2019 16:00-16:50 (MS 6221) Omer Mermelstein (University of Wisconsin - Madison) TBA Abstract. TBAHide Friday Feb 08 2019 16:00-16:50 (MS 6221) Adam Day (Victoria University of Wellington) TBA Abstract. TBAHide Friday Jan 25 2019 16:00-16:50 (MS 6221) Lynn Scow (California State University, San Bernardino) TBA Abstract. TBAHide Friday Jan 11 2019 08:30-09:20 (MS 6221) Szymon Toruńczyk (University of Warsaw) TBA Abstract. TBAHide

# Logic Colloquium: 09/1/2014 - 12/17/2018

 Friday Nov 30 2018 16:00-16:50 (MS 6221) Nick Ramsey (UCLA) Kim-independence and NSOP1 theories Abstract. Shelah's work on saturation spectra, Hrushovski on PAC structures, and Cherlin-Hrushovski on quasi-finite structures gave the initial impetus for the development of simple theories. A general theory, which unified and explained these different lines of research, was developed by Kim and Pillay using the notion of non-forking independence, which in turn spawned a remarkably rich line of model-theoretic research. In my talk, we will describe a parallel theory for the broader class of NSOP1 theories centered around the notion of Kim-independence and the applications that this theory made possible. We will survey results in a series of papers joint with Artem Chernikov, Itay Kaplan, Alex Kruckman, and Saharon Shelah (though not all at once).Hide Friday Nov 16 2018 16:00-16:50 (MS 6221) Lynn Scow (California State University, San Bernardino) Transfer of the Ramsey property - CANCELLED Abstract. For $L$-structures $B$, $C$ we use the notation ${C choose B}$ to denote the set of all substructures of $C$ isomorphic to $B$. We say that a countable, locally finite structure $I$ ordered by a relation $<$ has RP (the Ramsey property) if for all $A_0, B_0$ in age$(I)$ and integers $k geq 1$ there is some $C_0$ in age$(I)$ such that $C_0 rightarrow (B_0)^{A_0}_k$. In other words, for all functions $c: {C_0 choose A_0} rightarrow k$ there is some $B' subseteq C_0$, $B' cong B_0$ such that $c$ restricted to ${B' choose A_0}$ is a constant function. We will approach the question of when RP transfers from one countable structure to another, where these structures are in possibly different languages. We will look at universal algebraic and model theoretic criteria.Hide Friday Nov 02 2018 16:00-16:50 (MS 6221) Douglas Ulrich (UC Irvine) Generalized Amalgamation and Chromatic Numbers Abstract. Let $T_{k+1, k}$ denote the theory of the k-ary, k+1-clique free random hypergraph, for k >= 3. Malliaris and Shelah have famously proven that $T_{k+1, k}$ is not below $T_{k'+1, k'}$ in Keisler's order, whenever k+1 < k'; hence, Keisler's order has infinitely many classes. I have since improved the combinatorics to obtain the same result whenever k < k', and I obtain model-theoretic upper and lower bounds for the relevant dividing lines detected by Keisler's order. These bounds correspond to various kinds of k-dimensional amalgamation properties. The combinatorics involved is rather technical; however, the model-theoretic upper and lower bounds are not. I aim to introduce and motivate them; in particular, we will explore a connection between generalized amalgamation properties and the chromatic numbers of hypergraphs of partial types. It is open if the various k-dimensional amalgamation properties we introduce are equivalent.Hide Friday Oct 19 2018 16:00-16:50 (MS 6221) Sam Buss (UC San Diego) Bounded Arithmetic, Expanders, and Monotone Propositional Proofs Abstract. This talk discusses a new combinatorial proof of the existence of expander graphs, which can be carried out in the bounded arithmetic theory VNC$^1$ corresponding to alternating linear time. As an application, we prove that the monotone propositional sequent calculus polynomially simulates the full propositional sequent calculus. Prior to this, only a quasipolynomial simulation was known. Joint work with Valentine Kabanets, Antonina Kolokolova, and Michal Koucky.Hide Friday Oct 05 2018 16:00-16:50 (MS 6221) Byunghan Kim (Yonsei University, Seoul) On the number of countable NSOP$_1$ theories without weight $omega$. Abstract. Lachlan's problem is asking whether any countable theory $T$ with \$1