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The chapters of this volume all have their own level of presentation. The topics have been chosen based on the active research interest associated with them. Since the interest in some topics is older than that in others, some presentations contain fundamental definitions and basic results while others relate very little of the elementary theory behind them and aim directly toward an exposition of advanced results. Presentations of the latter sort are in some cases restricted to a short survey of recent results (due to the complexity of the methods and proofs themselves). Hence the variation in level of presentation from chapter to chapter only reflects the conceptual situation itself. One example of this is the collective efforts to develop an acceptable theory of computation on the real numbers. The last two decades has seen at least two new definitions of effective operations on the real numbers.
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J. Barwise, L. Blum, M. Shub, S. Smale, Fr Drake, Ss Wainer, E. Engeler, Hm Friedman, Ro Gandy & Cme Yates, 358 PG. Hinman.
Sc Kleene, El Post, M. Kline, M. Lerman, L. Lowenheim, D. Normann, P. Odifreddi, G. Peano, Cs Peirce & R. Penrose, R. PETER  Uber den Zussammenhang der verschiedenen Begriffe der rekursiven Funktion, Math. Ann.
M. Magidor, S. Shelah, J. Stavi, M. Mytilinaios, Ta Slaman, Jb Paris & H. la KirbyRogers Jr, Ge Sacks and Sg Simpson  the Oz-Finite Injury Method, Ann. Math. Logic, 4, Pp. 323-367.
Yn Moschovakis, J. Moldestad, V. Stoltenberg-Hansen, Jv Tucker, E. Nagel, P. Suppes, A. Tarski & Ra Platek, He Rose and Jc Shepherdson.
D. Scott, Vl Selivanov, Shoenfield Jr & Ra Shore, E. PALIUTIN  Addendum to the Paper of Ershov , Algebra I Logika, 14, Pp. 284-287; Transl. 14.
J. Stillwell, V. Stoltenberg-Hansen & Jv Tucker, C. TRETKOFF  Complexity, Combinatorial Group Theory and the Language of Palutators, Theoret. Comput. Sci., 56. Pp. 253-275. [REVIEW]
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