Infinite games and special Baire space extensions
نویسندگان
چکیده
منابع مشابه
Playing Games in the Baire Space
We solve a generalized version of Church’s Synthesis Problem where a play is given by a sequence of natural numbers rather than a sequence of bits; so a play is an element of the Baire space rather than of the Cantor space. Two players Input and Output choose natural numbers in alternation to generate a play. We present a natural model of automata (“N-memory automata”) equipped with the parity ...
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We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space [10] admits a Borel extension. (2) If the continuum is not a real-valued measurable cardinal then every Baire measure on the M. E. Rudin Dowker space [16] admits a Borel extension. Consequently, Balogh’s space [3] remains as the only candidate to be a ZFC counterexample to the measure extension problem of the three presently kn...
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Let k be a number field. A natural question is: Does k admit an infinite unramified extension? The answer is no, if the root discriminant of k is less than Odlyzko’s bounds. The answer is yes, if k fails the test of Golod-Shafarevic for a prime number p. In that case, we know that there exists an infinite unramified p-extension L over k. But generally it is fairly difficult to determin whether ...
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The problem of solvability of infinite games is closely connected with the classical question of uniformization of relations by functions of a given class. We work out this connection and discuss recent results on infinite games that are motivated by the uniformization problem. The fundamental problem in the effective theory of infinite games was posed by Church in 1957 (“Church’s Problem”; see...
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A function from Baire space N to the natural numbers N is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer-operation (i.e. inductively defined neighbourhood function); the other is a fu...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1974
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1974.55.483