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001 sulb-eb0023369
003 BD-SySUS
005 20160413122347.0
007 cr nn 008mamaa
008 131017s2013 gw | s |||| 0|eng d
020 _a9783319013336
_9978-3-319-01333-6
024 7 _a10.1007/978-3-319-01333-6
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aHardin, Christopher S.
_eauthor.
245 1 4 _aThe Mathematics of Coordinated Inference
_h[electronic resource] :
_bA Study of Generalized Hat Problems /
_cby Christopher S. Hardin, Alan D. Taylor.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2013.
300 _aXI, 109 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v33
505 0 _a1. Introduction -- 2. The Finite Setting -- 3. The Denumerable Setting: Full Visibility -- 4. The Denumerable Setting: One-Way Visibility -- 5. Dual Hat Problems and the Uncountable -- 6. Galvin's Setting: Neutral and Anonymous Predictors -- 7. The Topological Setting -- 8. Universality of the μ-Predictor -- 9. Generalizations and Galois-Tukey Connections -- Bibliography -- Index.
520 _aTwo prisoners are told that they will be brought to a room and seated so that each can see the other. Hats will be placed on their heads; each hat is either red or green. The two prisoners must simultaneously submit a guess of their own hat color, and they both go free if at least one of them guesses correctly. While no communication is allowed once the hats have been placed, they will, however, be allowed to have a strategy session before being brought to the room. Is there a strategy ensuring their release? The answer turns out to be yes, and this is the simplest non-trivial example of a “hat problem.” This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points. Topics range from hat problems that are accessible to everyone willing to think hard, to some advanced topics in set theory and infinitary combinatorics. For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense. The monograph progresses from topics requiring fewer prerequisites to those requiring more, with most of the text being accessible to any  graduate student in mathematics. The broad range of readership  includes researchers, postdocs, and graduate students in the fields of  set theory, mathematical logic, and combinatorics, The hope is that this book will bring together mathematicians from different areas to  think about set theory via a very broad array of coordinated inference problems.
650 0 _aMathematics.
650 0 _aGame theory.
650 0 _aMathematical logic.
650 0 _aTopology.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aTopology.
650 2 4 _aGame Theory, Economics, Social and Behav. Sciences.
700 1 _aTaylor, Alan D.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319013329
830 0 _aDevelopments in Mathematics,
_x1389-2177 ;
_v33
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-01333-6
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c45461
_d45461