Lightface analytic game
Encyclopedia
In descriptive set theory
, a lightface analytic game is a game whose payoff set A is a
subset
of Baire space
; that is, there is a tree T on
which is a computable subset of 
, such that A is the projection of the set of all branches of T.
The determinacy
of all lightface analytic games is equivalent to the existence of 0#
.
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
, a lightface analytic game is a game whose payoff set A is a
subsetSubset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
of Baire space
Baire space (set theory)
In set theory, the Baire space is the set of all infinite sequences of natural numbers with a certain topology. This space is commonly used in descriptive set theory, to the extent that its elements are often called “reals.” It is often denoted B, N'N, or ωω...
; that is, there is a tree T on
which is a computable subset of , such that A is the projection of the set of all branches of T.The determinacy
Determinacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.-Games:...
of all lightface analytic games is equivalent to the existence of 0#
Zero sharp
In the mathematical discipline of set theory, 0# is the set of true formulas about indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers , or as a subset of the hereditarily finite sets, or as a real number...
.