3 results
Chapter 12 - LSA from PFA
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- Book:
- The Largest Suslin Axiom
- Published online:
- 07 June 2024
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- 27 June 2024, pp 335-384
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NOTE ON
$\mathsf {TD} + \mathsf {DC}_{\mathbb {R}}$ IMPLYING 
$\mathsf {AD}^{L(\mathbb {R})}$
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 89 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 04 January 2024, pp. 211-217
- Print publication:
- March 2024
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A short core model induction proof of
$\mathsf {AD}^{L(\mathbb {R})}$ from 
$\mathsf {TD} + \mathsf {DC}_{\mathbb {R}}$.
Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
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- Journal:
- Canadian Journal of Mathematics / Volume 66 / Issue 4 / 01 August 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 903-923
- Print publication:
- 01 August 2014
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In this paper, we show that the failure of the unique branch hypothesis
$\left( \text{UBH} \right)$ for tame trees implies that in some homogenous generic extension of 
$V$ there is a transitive model 
$M$ containing Ord 
$\cup \mathbb{R}$ such that 
$M\,\vDash \,\text{A}{{\text{D}}^{+}}\,+\,\Theta \,>\,{{\theta }_{0}}$. In particular, this implies the existence (in $V$) of a non-tame mouse. The results of this paper significantly extend J. R. Steel's earlier results for tame trees.
