Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

index 309science and infinity overview, 19–47Scott set, 123Scott’s theorem, 112SDE. See Strong Diverse Exactness axiomSegantini, Giovanni, 208, 210self-similarity, 67self-transcendence, 31, 46serial endlessness/finiteness, 297serial interminability, 255Set Theorists Cosmological Principle(Woodin), 3set theory. See also Cantor, Georg; continuumhypothesis; infinite sets; universe of sets;ZFC 0 set theory; ZFC set theory; ZF settheory; Z set theoryaxioms of, 91–92, 97–102causal set theory, 168–69consistency of, 4defined, 2, 89finite, 92–96Gödel-Bernays class-set theory, 10, 38and infinite entities, 13large cardinal axioms in, 97–102mathematical discussion of, 89and mathematical infinity, 65–67, 69–70,94vs. the physical world, 3reflection principle in, 11skeptic’s view of, 94–97, 117transfinite, 5, 10Shor, Peter, 73Sikorski, Roman, 223Simplicius of Cilicia, 20, 170singularities, 7–8, 185–87, 186n8, 194n2,218–28, 267skeptic’s view of set theory, 94–97, 117Sloan Digital Sky Survey, 195n3smallness. See infinities of the small“Some Considerations on Infinity in Physics”(Rovelli), 167–75space. See finite space; infinite space; physicalinfinity; physical space; physical universespace curvature, 5–6, 69, 177, 197–203, 207,213, 223spacetime(s)b-boundary of, 222–23in bubble theory, 181–82, 182f, 187causal boundary of, 220, 223conformal transformations in, 219–20curves in, 220–23decomposition of, 7, 181–82, 181f, 183n4,194n2, 220–22and FLRW, 196–97Friedmann, 223in general relativity theory, 8, 168, 176, 224homogeneous and isotropic, 176–79, 181,196illustrations, 181findivisibility of, 181and infinity, 8, 176, 214, 219–20, 224,227and inflationary cosmology, 182Minkowski, 197multiverse of, 6mutually inaccessible, 6in the observable universe, 205, 210and omnipotent beings, 244and Penrose diagrams, 220in Planck length, 8singularities in, 7–8, 219–23slicing of, 183–84, 186structure in, 180, 220–22timelike infinities in, 220transcended, 8, 227two-component, 219volume of, 188sparse theories of God, 237–39spatial infinity. See infinite spacespeculation in physics, 96, 173–75, 204, 218,224–26speed of light, 7, 178, 180–83, 182f, 196Spinoza, Baruch, 39, 43, 43n116, 271STAR axiom, 163statesfinite vs. infinite number of, 7, 176, 188–91Hamiltonian, 188microstates, 188, 189n11steady-state model, 178, 185, 200n17and the Turing machine, 70–71steady-state model, 178, 185, 200n17Steinhardt, Paul, 7Steinhaus, Hugo, 95Stoeger, Bill, 283n22Stoic thought, 258–59string theory, 168–69, 196n10, 225strong cosmological principle, 196, 200, 205Strong Diverse Exactness axiom (SDE), 131,138–40, 145, 148–51, 159, 161–64Strong Unlimited Improvement axiom (SUI),131, 138–41, 143, 146, 163–64SUI. See Strong Unlimited Improvement axiomSunyaev-Zel’dovich effect, 201–2, 201n18supercompact cardinals, 113–16superexponentiation, 82, 84–85superstring theory, 196n10, 225Super Strong Diverse Exactness axiom (SSDE),131, 138–40, 143, 145–48, 163Swinburne, Richard, 236, 238