Institution-independent Ultraproducts

Ultraproducts and possible worlds semantics in institutions

We develop possible worlds (Kripke) semantics at the categorical abstract model theoretic level provided by the so-called ‘institutions’. Our general abstract modal logic framework provides a method for systematic Kripke semantics extensions of logical systems from computing science and logic. We also extend the institution-independent method of ultraproducts of [R. Diaconescu, Institution-inde...

Kiddie Talk: Ultraproducts and Szeméredi’s Theorem

As promised, this talk will not assume any knowledge of ultrafilters, ultraproducts, or any model theory. The plan is as follows: (1) Ultrafilters (2) Ultraproducts (3) Joke (4) What are ultraproducts good for? (5) Szeméredi’s theorem via ultraproducts References: Mostly Terence Tao’s various blog notes on ultraproducts. For model theory, see David Marker’s Model Theory: An Introduction for a v...

Applications of Pcf Theory Sh589

Abstract. We deal with several pcf problems; we characterize another version of exponentiation: number of κ-branches in a tree with λ nodes, deal with existence of independent sets in stable theories, possible cardinalities of ultraproducts and the depth of ultraproducts of Boolean Algebras. Also we give cardinal invariants for each λ with a pcf restriction and investigate further TD(f). The se...

Nonstandard Analysis and Ultraproducts in Banach Spaces and Functional Analysis Lecture 1: Nonstandard Analysis and Ultraproducts of Structures

Ultraproducts of measure preserving actions and graph combinatorics

Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.