J. P. Aguilera

activity

20152023

most citedUnsound Inferences Make Proofs Shorter

21 citations · 43 across the 14 of their papers we have counts for

collaborators

Showing 2019Show all

6 papers · 1 filter

math.LO2019★ 1 cited

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.

math.LO2019★ 7 cited

The consistency strength of long projective determinacy

Juan P. Aguilera, Sandra Müller

We determine the consistency strength of determinacy for projective games of length $ω^{2}$ . Our main theorem is that $Π_{n + 1}^{1}$ -determinacy for games of length $ω^{2}$ imp…

math.LO2019★ 3 cited

Extending Aanderaa's classical result that $π_{1}^{1} < σ_{1}^{1}$ , we determine the order between any two patterns of iterated $Σ_{1}^{1}$ - and $Π_{1}^{1}$ -reflection. We show that this \emph{linea…

math.LO2019

$F_{σ}$ Games and Reflection in $L (R)$

J. P. Aguilera

It is shown that determinacy of $F_{σ}$ games of length $ω^{2}$ is equivalent to the existence of a transitive model of KP + AD which contains the reals and reflects $Π_{1}$ facts about…

math.LO2019

Long Borel Games

J. P. Aguilera

It is shown that Borel games of length $ω^{2}$ are determined if, and only if, for every countable ordinal $α$ , there is a fine-structural, countably iterable extender model of Zerme…

Projective Games on the Reals

Determined Admissible Sets

The consistency strength of long projective determinacy

The Order of Reflection

Fσ​ Games and Reflection in L(R)

Long Borel Games

$F_{σ}$ Games and Reflection in $L (R)$