Abstract
The paper is concerned with reflexive points of relations. The significance of reflexive points in the context of indeterminate recursion principles is shown.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Berman, J., Blok, W., [1989], ‘Generalizations of Tarski’s fixed-point theorem for order varieties of complete meet semilattices’, Order, 5(4): 381–392.
Cai, J., Paige, R., [1992], ‘Languages polynomial in the input plus output’, in Second International Conference on Algebraic Methodology and Software Technology (AMAST 91), Springer Verlag, London, pp. 287–300.
Chang, C.C., Keisler, H.J., [1973], Model Theory, North-Holland and American Elsevier, Amsterdam–London–New York.
Czelakowski, J., [2006], ‘Fixed-points for relations and the back and forth method’, Bulletin of the Section of Logic, 35(2/3): 63–71.
Davey, B.A., Priestley, H., [2002] Introduction to Lattices and Order, 2nd ed., Cambridge University Press, Cambridge.
Desharnais, J., Möller, B., [2005], ‘Least reflexive points of relations’, Higher-Order and Symbolic Computation, 18: 51–77.
Dugundji, J., Granas, A., [1982], Fixed Point Theory, Monografie Matematyczne, vol. 61, PWN, Warsaw.
Fujimoto, T., [1984], ‘An extension of Tarski’s fixed point theorem and its application to isotone complementarity problems’, Mathematical Programming, 28: 116–118.
Goebel, K., Kirk, W.A., [1990], Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge.
Gunter, C.A., Scott, D.S., [1990], ‘Semantic domains’, in Van Leeuwen, J. (Managing Editor), Handbook of Theoretical Computer Science, The MIT Press/Elsevier, Amsterdam, New York-Oxford-Tokyo/Cambridge, Massachusetts, pp. 634–674.
Kirk, W.A., Sims, B. (eds.), [2001], Handbook of Metric Fixed Point Theory, Kluwer, Dordrecht, Boston–London.
Kleene, S.C., [1952], Introduction to Metamathematics, Van Nostrand.
Kunen, K., [1999], Set Theory. An Introduction to Independence Proofs, Elsevier, Amsterdam–Lausanne–New York.
Markowsky, G., [1976], ‘Chain-complete posets and directed sets with applications’, Algebra Universalis, 6: 53–68.
Moschovakis, Y.N., [1994], Notes on Set Theory, Springer-Verlag, New York–Berlin.
Tarski, A., [1955], ‘A lattice-theoretical fixpoint theorem and its applications’, Pacific Journal of Mathematics, 5: 285–309.
Wright, J., Wagner, E., Thatcher, J., [1978], ‘A uniform approach to inductive posets and inductive closure’, Theoretical Computer Science, 7: 57–77.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Czelakowski, J. (2009). Monotone Relations, Fixed Points and Recursive Definitions. In: Makinson, D., Malinowski, J., Wansing, H. (eds) Towards Mathematical Philosophy. Trends in Logic, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9084-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4020-9084-4_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-9083-7
Online ISBN: 978-1-4020-9084-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)