Geodesic
On rigid relation principles in set theory without the axiom of choice
Paul Howard 1   ; Eleftherios Tachtsis 2
1 Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197, U.S.A.
2 Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece
Fundamenta Mathematicae, Tome 232 (2016) no. 3, pp. 199-226 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the deductive strength of the following statements: $\mathsf{RR}$: every set has a rigid binary relation, $\mathsf{HRR}$: every set has a hereditarily rigid binary relation, $\mathsf{SRR}$: every set has a strongly rigid binary relation, in set theory without the Axiom of Choice. $\mathsf{RR}$ was recently formulated by J. D. Hamkins and J. Palumbo, and $\mathsf{SRR}$ is a classical (non-trivial) $\mathsf{ZFC}$-result by P. Vopěnka, A. Pultr and Z. Hedrlín.
DOI : 10.4064/fm960-12-2015
Keywords: study deductive strength following statements mathsf every set has rigid binary relation mathsf hrr every set has hereditarily rigid binary relation mathsf srr every set has strongly rigid binary relation set theory without axiom choice mathsf recently formulated nbsp nbsp hamkins nbsp palumbo mathsf srr classical non trivial mathsf zfc result nbsp vop nka nbsp pultr nbsp hedrl

Paul Howard  1   ; Eleftherios Tachtsis  2

1 Department of Mathematics Eastern Michigan University Ypsilanti, MI 48197, U.S.A.
2 Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece 
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Paul Howard; Eleftherios Tachtsis. On rigid relation principles in set theory without the axiom of choice. Fundamenta Mathematicae, Tome 232 (2016) no. 3, pp. 199-226. doi: 10.4064/fm960-12-2015

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