caa a22 4500 388039531 CHVBK 20180307125017.0 cr unu---uuuuu 161130e199803 xx s 000 0 eng 10.2307/2586591 doi S002248120001536X pii (NATIONALLICENCE)cambridge-10.2307/2586591 Uniformization and skolem functions in the class of trees [Elektronische Daten] The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have definable Skolem functions (by a monadic formula with parameters)? This continues [6] where the question was asked only with respect to choice functions. A natural subclass is defined and proved to be the class of trees with definable Skolem functions. Along the way we investigate the spectrum of definable well orderings of well ordered chains. Copyright © Association for Symbolic Logic 1998 Lifsches Shmuel Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: sam@math.huji.ac.il Shelah Saharon Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 103-127 0022-4812 63:1<103 1998 63 JSL https://doi.org/10.2307/2586591 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586591 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lifsches Shmuel Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: sam@math.huji.ac.il NATIONALLICENCE 700 1- Shelah Saharon Institute of Mathematics, The Hebrew University, Jerusalem, Israel, E-mail: shelah@math.huji.ac.il NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/1(1998-03), 103-127 0022-4812 63:1<103 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge