J. P. Aguilera

activity

20192021

collaborators

10 papers

math.LO2022

Functorial Fast-Growing Hierarchies

J. P. Aguilera, F. Pakhomov, A. Weiermann

Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplicati…

math.LO2021

The $Π_{2}^{1}$ Consequences of a Theory

Juan P. Aguilera, Fedor Pakhomov

We develop the abstract framework for a proof-theoretic analysis of theories with scope beyond ordinal numbers, resulting in an analog of Ordinal Analysis aimed at the study of the…

math.LO2020

Ackermann and Goodstein go functorial

Juan P. Aguilera, Anton Freund, Michael Rathjen +1

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…

math.LO2020

Long Games and $σ$ -Projective Sets

Juan P. Aguilera, Sandra Müller, Philipp Schlicht

We prove a number of results on the determinacy of $σ$ -projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under compleme…

math.LO2019

Projective Games on the Reals

Juan P. Aguilera, Sandra Müller

Let $M_{n}^{♯} (R)$ denote the minimal active iterable extender model which has $n$ Woodin cardinals and contains all reals, if it exists, in which case we denote by $M_n(…

math.LO2019

Determined Admissible Sets

Juan P. Aguilera

It is shown, from hypotheses in the region of $ω^{2}$ Woodin cardinals, that there is a transitive model of KP + AD $_{R}$ containing all reals.