Zobrazeno 1 - 10
of 198
pro vyhledávání: '"Weiermann, Andreas"'
Publikováno v:
The Bulletin of Symbolic Logic, 2024 Mar 01. 30(1), 1-19.
Externí odkaz:
https://www.jstor.org/stable/27294832
In this paper, we derive a novel optimal image transport algorithm over sparse dictionaries by taking advantage of Sparse Representation (SR) and Optimal Transport (OT). Concisely, we design a unified optimization framework in which the individual im
Externí odkaz:
http://arxiv.org/abs/2311.01984
We prove that Buchholz's system of fundamental sequences for the $\vartheta$ function enjoys various regularity conditions, including the Bachmann property. We partially extend these results to variants of the $\vartheta$ function, including a versio
Externí odkaz:
http://arxiv.org/abs/2203.07758
Autor:
Fernández-Duque, David, Joosten, Joost J., Pakhomov, Fedor, Papafilippou, Konstnatinos, Weiermann, Andreas
Japaridze's provability logic $GLP$ has one modality $[n]$ for each natural number and has been used by Beklemishev for a proof theoretic analysis of Peano aritmetic $(PA)$ and related theories. Among other benefits, this analysis yields the so-calle
Externí odkaz:
http://arxiv.org/abs/2112.07473
We define a variant of the Goodstein process based on fast-growing functions and show that it terminates, but this fact is not provable in Kripke-Platek set theory or other theories of strength the Bachmann-Howard ordinal. We moreover show that this
Externí odkaz:
http://arxiv.org/abs/2111.15328
Publikováno v:
In Annals of Pure and Applied Logic August-September 2024 175(8)
Publikováno v:
Pacific J. Math. 313 (2021) 251-291
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These variants differ from the usual Goodstein theorem in that they (necess
Externí odkaz:
http://arxiv.org/abs/2011.03439
Autor:
Weiermann, Andreas
By combining classical results of B\"uchi, some elementary Tauberian theorems and some basic tools from logic and combinatorics we show that every ordinal $\alpha$ with $\varepsilon_0\geq \alpha\geq \omega^\omega$ satisfies a natural monadic second o
Externí odkaz:
http://arxiv.org/abs/2007.14111
Autor:
Weiermann, Andreas
We analyze several natural Goodstein principles which themselves are defined with respect to the Ackermann function and the extended Ackermann function. These Ackermann functions are well established canonical fast growing functions labeled by ordina
Externí odkaz:
http://arxiv.org/abs/2007.09086
The original Goodstein process proceeds by writing natural numbers in nested exponential $k$-normal form, then successively raising the base to $k+1$ and subtracting one from the end result. Such sequences always reach zero, but this fact is unprovab
Externí odkaz:
http://arxiv.org/abs/2004.09117