Zobrazeno 1 - 10
of 1 498
pro vyhledávání: '"Bącal P"'
We study the question of when a given countable ordinal $\alpha$ is $\Sigma^1_n$- or $\Pi^1_n$-reflecting in models which are neither $\mathsf{PD}$ models nor the constructible universe, focusing on generic extensions of $L$. We prove, amongst other
Externí odkaz:
http://arxiv.org/abs/2311.12533
Autor:
Sakai, Hiroshi, Switzer, Corey Bacal
We study a family of variants of Jensen's subcomplete forcing axiom, $\mathsf{SCFA}$ and subproper forcing axiom, $\mathsf{SubPFA}$. Using these we develop a general technique for proving non-implications of $\mathsf{SCFA}$, $\mathsf{SubPFA}$ and the
Externí odkaz:
http://arxiv.org/abs/2308.16276
Autor:
Fischer, Vera, Switzer, Corey Bacal
We prove that the generic maximal independent family obtained by iteratively forcing with the Mathias forcing relative to diagonalization filters is densely maximal. Moreover, by choosing the filters with some care one can ensure the family is select
Externí odkaz:
http://arxiv.org/abs/2306.09809
A family $\mathcal{A} \subseteq [\omega]^\omega$ such that for all finite $\{X_i\}_{i\in n}\subseteq \mathcal A$ and $A \in \mathcal{A} \setminus \{X_i\}_{i\in n}$, the set $A \setminus \bigcup_{i \in n} X_i$ is infinite, is said to be ideal independ
Externí odkaz:
http://arxiv.org/abs/2304.04651
Publikováno v:
Communications Earth & Environment, Vol 5, Iss 1, Pp 1-8 (2024)
Abstract Shifts in the magnesium to calcium ratio of seawater in the geological history are thought to have profoundly affected biomineralization of marine invertebrates, including some echinoderms, which changed their skeletal mineralogy from high-m
Externí odkaz:
https://doaj.org/article/d425d4dbc4724ac699b4ad151f4e610a
Publikováno v:
Acta Palaeontologica Polonica, Vol 68, Iss 2, Pp 217-225 (2024)
An interesting case of a caries-affected area where bacterial remains were plausibly preserved in situ was found in an isolated tooth of the Plio-Pleistocene dormouse Glis sackdillingensis (Rodentia, Gliridae). The sample is 2.9–2.6 million years o
Externí odkaz:
https://doaj.org/article/d22ec9e4bbb7405f96b070d8cf4bb9ad
Autor:
Fischer, Vera, Switzer, Corey Bacal
We provide a general preservation theorem for preserving selective independent families along countable support iterations. The theorem gives a general framework for a number of results in the literature concerning models in which the independence nu
Externí odkaz:
http://arxiv.org/abs/2208.09854
A family $\mathscr{I} \subseteq [\omega]^\omega$ such that for all finite $\{X_i\}_{i\in n}\subseteq \mathcal I$ and $A \in \mathscr{I} \setminus \{X_i\}_{i\in n}$, the set $A \setminus \bigcup_{i < n} X_i$ is infinite, is said to be ideal independen
Externí odkaz:
http://arxiv.org/abs/2206.14019
Autor:
Switzer, Corey Bacal
Define the special tree number, denoted $\mathfrak{st}$, to be the least size of a tree of height $\omega_1$ which is neither special nor has a cofinal branch. This cardinal had previously been studied in the context of fragments of $\mathsf{MA}$ but
Externí odkaz:
http://arxiv.org/abs/2203.04186
Autor:
Switzer, Corey Bacal
Generalizing the proof for Sacks forcing, we show that the $h$-perfect tree forcing notions introduced by Goldstern, Judah and Shelah preserve selective independent families even when iterated. As a result we obtain new proofs of the consistency of $
Externí odkaz:
http://arxiv.org/abs/2202.12046