We review a paper by Shelah and Vasey (2018), and obtain some properties of an AEC K assuming $\aleph_0$-stability. The main result is: under tameness, amalgamation and no maximal models in $\aleph_0$, there is a good $\aleph_0$-frame and a superlimit in $\aleph_1$.

, Shelah’s eventual categoricity conjecture in universal classes,

Published: February 24, 2022

We present Sebastien Vasey’s proof of Shelah’s categoricity conjecture in universal classes. First we change the substructure relation of the given class to obtain an AEC with better properties, except that the union axiom might not hold. To prove that the union axiom holds, we use the independence framework AxFr developed by Shelah, build an “independent” tree assuming the failure of union, and contradict stability.

, Some relations between $\mu$-abstarct elementary classes and accessible categories

Published: May 06, 2022

We will investigate the relationship between μ-abstract elementary classes, which are generalizations of AECs by requiring only μ-directed unions to exist, and accessible categories, which are categories generated by certain “small” objects under μ-directed colimits.

, Deligne’s completeness theorem

Published: February 03, 2023

Deligne’s theorem states that any coherent topos has enough points. The theorem can be viewed as a completeness theorem when specialized to the classifying topos of a geometric theory. First we explain this connection to logic and then present a proof of Deligne’s theorem.

, An NIP-like notion for abstract elementary classes

Published: March 28, 2023

We propose an analogue definition of No Independence Property (NIP) for abstract elementary classes (AECs) that coincides with NIP in first order model theory, where the class is elementary. As we have no formulas in this context we work with Galois types. We construct a forking-like relation on AECs with NIP. Our work can be viewed as a new chapter in the neo-stability of AECs, building on Armida-Mazari’s work.

, An NIP-like notion in abstract elementary classes

Published: April 04, 2023

We propose an analogue definition of No Independence Property (NIP) for abstract elementary classes (AECs) that coincides with NIP when the class is elementary. We construct a forking-like relation on AECs with NIP, and show that its negation leads to being able to encode subsets.

teaching

, Teaching at CMU

Teaching Assistant Carnegie Mellon University, Department of Mathematical Sciences

Differential and Integral Calculus, Matrix Algebra with Applications, Integration and Approximation, Advanced Math Support Center

, Grading at CMU

Grading Carnegie Mellon University, Department of Mathematical Sciences

Algebraic Structures, Matrix Algebra, Set Theory

Wentao Yang

Posts by Collection

portfolio

, Portfolio item number 1

, Portfolio item number 2

publications

Wentao Yang, An NIP-like notion in abstract elementary classes

Wentao Yang, On successive categoricity, stability and NIP in abstract elementary classes

Marcos Mazari-Armida and Wentao Yang, Building models in small cardinals in local abstract elementary classes

Marcos Mazari-Armida, Sebastien Vasey and Wentao Yang, On Stability and Existence of Models in Abstract Elementary Classes

talks

, $\aleph_0$-stable AECs