@article{Givant:2006va,
    Abstract = {A variable-free, equational logic {\$}{$\backslash$}mathcal{\{}L{\}}\^{}{$\backslash$}times{\$}based on the calculus of relations (a theory of binary relations developed by De Morgan, Peirce, and Schr{\"o}der during the period 1864--1895) is shown to provide an adequate framework for the development of all of mathematics. The expressive and deductive powers of {\$}{$\backslash$}mathcal{\{}L{\}}\^{}{$\backslash$}times{\$}are equivalent to those of a system of first-order logic with just three variables. Therefore, three-variable first-order logic also provides an adequate framework for mathematics. Finally, it is shown that a variant of {\$}{$\backslash$}mathcal{\{}L{\}}\^{}{$\backslash$}times{\$}may be viewed as a subsystem of sentential logic. Hence, there are subsystems of sentential logic that are adequate to the task of formalizing mathematics.},
    Author = {Givant, Steven},
    Date = {2006/11/01},
    File = {The Calculus of Relations as a Foundation for Mathematics - Givant2006\_Article\_TheCalculusOfRelationsAsAFound.pdf},
    ISBN = {1573-0670},
    Journal = {Journal of Automated Reasoning},
    Number = {4},
    Pages = {277--322},
    Title = {The Calculus of Relations as a Foundation for Mathematics},
    URL = {https://doi.org/10.1007/s10817-006-9062-x},
    Volume = {37},
    Year = {2006},
    bdsk-url-1 = {https://doi.org/10.1007/s10817-006-9062-x},
    date-added = {2022-02-22 13:18:16 +0100},
    date-modified = {2022-02-22 13:18:16 +0100},
    id = {Givant2006},
    doi = {10.1007/s10817-006-9062-x}
}

@article{Givant:2006va, Abstract = {A variable-free, equational logic {\$}{$\backslash$}mathcal{{}L{}}\^{}{$\backslash$}times{\$}based on the calculus of relations (a theory of binary relations developed by De Morgan, Peirce, and Schr{\"o}der during the period 1864--1895) is shown to provide an adequate framework for the development of all of mathematics. The expressive and deductive powers of {\$}{$\backslash$}mathcal{{}L{}}\^{}{$\backslash$}times{\$}are equivalent to those of a system of first-order logic with just three variables. Therefore, three-variable first-order logic also provides an adequate framework for mathematics. Finally, it is shown that a variant of {\$}{$\backslash$}mathcal{{}L{}}\^{}{$\backslash$}times{\$}may be viewed as a subsystem of sentential logic. Hence, there are subsystems of sentential logic that are adequate to the task of formalizing mathematics.}, Author = {Givant, Steven}, Date = {2006/11/01}, File = {The Calculus of Relations as a Foundation for Mathematics - Givant2006_Article_TheCalculusOfRelationsAsAFound.pdf}, ISBN = {1573-0670}, Journal = {Journal of Automated Reasoning}, Number = {4}, Pages = {277--322}, Title = {The Calculus of Relations as a Foundation for Mathematics}, URL = {https://doi.org/10.1007/s10817-006-9062-x}, Volume = {37}, Year = {2006}, bdsk-url-1 = {https://doi.org/10.1007/s10817-006-9062-x}, date-added = {2022-02-22 13:18:16 +0100}, date-modified = {2022-02-22 13:18:16 +0100}, id = {Givant2006}, doi = {10.1007/s10817-006-9062-x} }