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Everything about Determinacy
Subfield of set theory
Determinacy is a subfield of game theory and set theory that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists. Determinacy was introduced by Gale and Stewart in 1950, under the name determinateness. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: DeterminacyA 5-minute orientation
- Skim a recent paper: The control of carpel determinacy pathway leads to sex determination in cucurbitsInfluential work since 2022
- Pick up a classic book: Trends in Set TheoryThe most-reprinted book on the subject
- Read the landmark paper: Borel DeterminacyCited 502 times
- Go sideways: Wadge hierarchyA closely related topic
- Go sideways: Lightface analytic gameA closely related topic
📖 Definitions
Noun The ability to be completely determined in a definite way; the quality of being determinate.
Noun (game theory) The study of the circumstances under which a game has a winning strategy.
🏆 Landmark papers (most cited)
Borel Determinacy
Monetary policy and price level determinacy in a cash-in-advance economy
Flowering-time genes modulate meristem determinacy and growth form in Arabidopsis thaliana
L3 syntactic transfer selectivity and typological determinacy: The typological primacy model
Analysis of linear determinacy for spread in cooperative models
Determinacy and Identification with Taylor Rules
Spreading speed and linear determinacy for two-species competition models
Price-level determinacy without control of a monetary aggregate
🆕 Influential since 2022
The control of carpel determinacy pathway leads to sex determination in cucurbits
Tomato CRABS CLAW paralogues interact with chromatin remodelling factors to mediate carpel development and floral determinacy
Two modes of gene regulation by TFL1 mediate its dual function in flowering time and shoot determinacy of Arabidopsis
Determinacy without the Taylor Principle
Gibberellin and miRNA156-targeted SlSBP genes synergistically regulate tomato floral meristem determinacy and ovary patterning
📚 Books worth reading
- 📕Trends in Set TheorySamuel Coskey, Grigor Sargsyan · 2020
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Wadge hierarchy In descriptive set theory, within mathematics, Wadge degrees are levels of complexity for sets of reals. Sets are compared by continuous reductions. The…
- Lightface analytic game In descriptive set theory, a lightface analytic game is an infinite two-player game of perfect information whose payoff set is a lightface analytic (Σ11)…
- Axiom of determinacy In mathematics, the axiom of determinacy (abbreviated as AD) is a possible axiom for set theory introduced by Jan Mycielski and Hugo Steinhaus in 1962…
- Borel determinacy theorem In descriptive set theory, the Borel determinacy theorem states that any Gale–Stewart game whose payoff set is a Borel set is determined, meaning that…
- Descriptive set theory In mathematics, descriptive set theory is the study of certain classes of subsets of the real line and other Polish spaces satisfying some sort of definability…
- Woodin cardinal In set theory, a Woodin cardinal (named for W. Hugh Woodin) is a cardinal number λ such that for all functions f:λ→λ, there exists a cardinal κ<λ with…
- Projective determinacy In mathematical logic, projective determinacy is the special case of the axiom of determinacy applying only to projective sets. The axiom of projective…
- L(R) In set theory, L(R) (pronounced L of R) is the smallest transitive inner model of ZF containing all the ordinals and all the reals. L(R) can be constructed…