Zobrazeno 1 - 10
of 322
pro vyhledávání: '"Väänänen, Jouko"'
We show, assuming PD, that every complete finitely axiomatized second order theory with a countable model is categorical, but that there is, assuming again PD, a complete recursively axiomatized second order theory with a countable model which is non
Externí odkaz:
http://arxiv.org/abs/2405.03428
Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal $\mu$, we prove the consistency of the existence of a wide $\mu^+$-Aronszajn tree, i.e. a tree of height and cardinality $\mu^+$ with no branches of length $\m
Externí odkaz:
http://arxiv.org/abs/2305.07880
We introduce three measures of complexity for families of sets. Each of the three measures, that we call dimensions, is defined in terms of the minimal number of convex subfamilies that are needed for covering the given family: for upper dimension, t
Externí odkaz:
http://arxiv.org/abs/2304.03354
Autor:
Väänänen, Jouko
Publikováno v:
in: Infinity and Truth, Edited by: Chitat Chong, Qi Feng, Theodore A Slaman, W Hugh Woodin, Lecture Notes Series of the Institute for Mathematical Sciences, World Scientific, vol. 25, 2014, 171-186
I have argued elsewhere that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and the latter first order, but second order logic is marred by reliance o
Externí odkaz:
http://arxiv.org/abs/2302.05947
Autor:
Väänänen, Jouko
Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to each other a
Externí odkaz:
http://arxiv.org/abs/2212.01658
Autor:
Väänänen, Jouko
Anonymity has gained notoriety in modern times as data about our actions and choices accumulates in the internet partly unbeknownst to us and partly by our own choice. Usually people wish some data about themselves were private while some other date
Externí odkaz:
http://arxiv.org/abs/2210.07834
Autor:
Hyttinen, Tapani, Väänänen, Jouko
It is well-known that the first order Peano axioms PA have a continuum of non-isomorphic countable models. The question, how close to being isomorphic such countable models can be, seems to be less investigated. A measure of closeness to isomorphism
Externí odkaz:
http://arxiv.org/abs/2208.13052