Previous talks this semester:
09.05.2019 , 10.15, room 105,
Arturo MartínezCelis (IMPAN),
Title: Choice vs Determinacy
Abstract: "We will discuss the concept of infinite game and winning strategies and we will present some examples, theorems and applications to topology. In particular we will prove that every uncountable Borel set has a homeomorphic copy of the Cantor set.
The axiom of determinacy (AD) states that for certain kind of games, the GaleStewart games, one player has always a winning strategy. The aim of this talk is to present the differences between the universes satisfying AD and the universes satisfying the axiom of choice."
26.04.2019 (Friday), 10.15, room 106,
Fulgencio Lopez (IMPAN),
Title: Compact extensions of first order logic, continuation from 16.04
Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Q_{n} to be "There is an uncountable subset with an ndimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so
is L(Q_{n}:n∈ N) (Magidor and Malitz). We will also discuss why this framework can
sometimes be useful for constructions of set theoretical structures.
16.04.2019 (Tuesday), 10.15, room 106,
Fulgencio Lopez (IMPAN),
Title: Compact extensions of first order logic
Abstract: We aim to provide an exhaustive proof of the results of Keisler and Magidor and Malitz about the compactness of certain extensions of first order logic. Keisler's Theorem refers to the extension L(Q) where Q is the quantifier "There is an uncountable subset with a one dimensional property", similarly we can define Q_{n} to be "There is an uncountable subset with an ndimensional property". We will show that L(Q) is compact (Keisler's Theorem) and, assuming diamond, so
is L(Q_{n}:n∈ N) (Magidor and Malitz). We will also discuss why this framework can
sometimes be useful for constructions of set theoretical structures.
Talks in the first semester of 201819.
Talks in the second semester of 201718.
Talks in the first semester of 201718.
Talks in the second semester of 201617.
Talks in the first semester of 201617.
Talks in the second semester of 201516.
Talks in the first semester of 201516.
Talks in the second semester of 201415.
Talks in the first semester of 201415.
Talks in the second semester of 201314.
Talks in the first semester of 201314.
Talks in the second semester of 201213.
Talks in the first semester of 201213.
Talks in the second semester of 201112.
Talks in the first semester of 201112.
