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INCOMPATIBILITY OF GENERIC HUGENESS PRINCIPLES
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- Journal:
- Bulletin of Symbolic Logic / Volume 29 / Issue 2 / June 2023
- Published online by Cambridge University Press:
- 01 February 2023, pp. 157-162
- Print publication:
- June 2023
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- Article
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GENERIC LARGE CARDINALS AS AXIOMS
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- Journal:
- The Review of Symbolic Logic / Volume 13 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 14 May 2019, pp. 375-387
- Print publication:
- June 2020
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GENERIC LARGE CARDINALS AND SYSTEMS OF FILTERS
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- Journal:
- The Journal of Symbolic Logic / Volume 82 / Issue 3 / September 2017
- Published online by Cambridge University Press:
- 08 September 2017, pp. 860-892
- Print publication:
- September 2017
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We introduce the notion of
${\cal C}$-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals. This provides a framework to develop the theory of extenders and towers in a more general and concise way. In this framework we investigate the topic of definability of generic large cardinals properties.
DENSE IDEALS AND CARDINAL ARITHMETIC
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- Journal:
- The Journal of Symbolic Logic / Volume 81 / Issue 3 / September 2016
- Published online by Cambridge University Press:
- 14 September 2016, pp. 789-813
- Print publication:
- September 2016
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From large cardinals we show the consistency of normal, fine, κ-complete λ-dense ideals on
${{\cal P}_\kappa }\left( \lambda \right)$ for successor κ. We explore the interplay between dense ideals, cardinal arithmetic, and squares, answering some open questions of Foreman.
