Cramer, Scott S. Inverse limit reflection and the structure of \(L(V_{{\lambda}+1})\). (English) Zbl 1371.03070 J. Math. Log. 15, No. 1, Article ID 1550001, 38 p. (2015). Summary: We extend the results of Laver on using inverse limits to reflect large cardinals of the form, there exists an elementary embedding \(L_\alpha (V_{\lambda+1}) \to L_{\alpha}(V_{\lambda+1})\). Using these inverse limit reflection embeddings directly and by broadening the collection of \(U(j)\)-representable sets, we prove structural results of \(L(V_{\lambda+1})\) under the assumption that there exists an elementary embedding \(j : L(V_{\lambda+1}) \to L(V_{\lambda+1})\). As a consequence we show the impossibility of a generalized inverse limit \(X\)-reflection result for \(X \subseteq V_{\lambda+1}\), thus focusing the study of \(L(\mathbb{R})\) generalizations on \(L(V_{\lambda+1})\). Cited in 1 ReviewCited in 7 Documents MSC: 03E55 Large cardinals Keywords:large cardinals; reflection; elementary embeddings; inverse limits; stationary sets; perfect sets PDFBibTeX XMLCite \textit{S. S. Cramer}, J. Math. Log. 15, No. 1, Article ID 1550001, 38 p. (2015; Zbl 1371.03070) Full Text: DOI References: [1] D. Gale and F. M. Stewart, Contributions to the Theory of Games, Annals of Mathematics Studies 2 (Princeton University Press, Princeton, NJ, 1953) pp. 245–266. [2] Kanamori A., Perspectives in Mathematical Logic, in: The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings (1994) · Zbl 0813.03034 [3] DOI: 10.1007/978-1-4020-5764-9_24 · Zbl 1198.03072 · doi:10.1007/978-1-4020-5764-9_24 [4] DOI: 10.1016/S0168-0072(97)00031-6 · Zbl 0890.03027 · doi:10.1016/S0168-0072(97)00031-6 [5] DOI: 10.1016/S0168-0072(00)00035-X · Zbl 0968.03060 · doi:10.1016/S0168-0072(00)00035-X [6] DOI: 10.1007/BFb0071699 · doi:10.1007/BFb0071699 [7] DOI: 10.1142/S021906131100102X · Zbl 1248.03069 · doi:10.1142/S021906131100102X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.