Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Asperó, David"'
Generalizations of Martin's Axiom, weak square, weak Chang's Conjecture, and a forcing axiom failure
Autor:
Aspero, David, Tananimit, Nutt
We prove that the forcing axiom $MA^{1.5}_{\aleph_2}(\mbox{stratified})$ implies $\Box_{\omega_1, \omega_1}$. Using this implication, we show that the forcing axiom $MM_{\aleph_2}(\aleph_2\mbox{-c.c.})$ is inconsistent. We also derive weak Chang's Co
Externí odkaz:
http://arxiv.org/abs/2212.07324
Autor:
Asperó, David, Golshani, Mohammad
We show that the Proper Forcing Axiom for forcing notions of size $\aleph_1$ is consistent with the continuum being arbitrarily large. In fact, assuming $GCH$ holds and $\kappa\geq\omega_2$ is a regular cardinal, we prove that there is a proper and $
Externí odkaz:
http://arxiv.org/abs/2209.01395
Autor:
Aspero, David, Viale, Matteo
We introduce bounded category forcing axioms for well-behaved classes $\Gamma$. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe $H_{\lambda_\Gamma^+}$ modulo forcing in $\Gam
Externí odkaz:
http://arxiv.org/abs/2101.03132
Autor:
Aspero, David, Mota, Miguel Angel
Measuring says that for e\-very sequence $(C_\delta)_{\delta<\omega_1}$ with each $C_\delta$ being a closed subset of $\delta$ there is a club $C\subseteq\omega_1$ such that for every $\delta\in C$, a tail of $C\cap\delta$ is either contained in or d
Externí odkaz:
http://arxiv.org/abs/2012.07843
We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $\theta>\kappa$ to get the consistency of the forcing axiom for $\kappa$-strongly proper fo
Externí odkaz:
http://arxiv.org/abs/1912.02130
Autor:
Asperó, David, Karagila, Asaf
Methods of Higher Forcing Axioms was a small workshop in Norwich, taking place between 10--12 of September, 2019. The goal was to encourage future collaborations, and create more focused threads of research on the topic of higher forcing axioms. This
Externí odkaz:
http://arxiv.org/abs/1912.02123
Autor:
Asperó, David, Schindler, Ralf
We show that Martin's Maximum${}^{++}$ implies Woodin's ${\mathbb P}_{\rm max}$ axiom $(*)$. This answers a question from the 1990's and amalgamates two prominent axioms of set theory which were both known to imply that there are $\aleph_2$ many real
Externí odkaz:
http://arxiv.org/abs/1906.10213
Autor:
Asperó, David, Golshani, Mohammad
Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which $GCH$ holds and all $\aleph_2$-Aronszajn trees are special and hence there are no $\aleph_2$-Souslin trees. This result answers a well-kno
Externí odkaz:
http://arxiv.org/abs/1809.07638
Autor:
Aspero, David, Krueger, John
We introduce Strong Measuring, a maximal strengthening of J. T. Moore's Measuring principle, which asserts that every collection of fewer than continuum many closed bounded subsets of $\omega_1$ is measured by some club subset of $\omega_1$. The cons
Externí odkaz:
http://arxiv.org/abs/1808.08596
Autor:
Asperó, David, Karagila, Asaf
Publikováno v:
The Review of Symbolic Logic 14 (2021) 225-249
We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to DC-preserving symmetr
Externí odkaz:
http://arxiv.org/abs/1806.04077