Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with aan orthomodular hermitanHermitian form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics?
minor typos corrected, made title into a question
Is Solèr’s theorem true in constructive mathematics?
Solèr’s theorem in constructive mathematics
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics?
Is Solèr’s theorem true in constructive mathematics?
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with an orthomodular Hermitian form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics?
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics? If so, what sets of real numbers/complex numbers/quaternions does Solèr’s theorem result in for the star division rings? In constructive mathematics, the notion of real numbers/complex numbers/quaternions bifurcates into many different incompatible sets depending upon the definition used to define the real numbers/complex numbers/quaternions.
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics? If so, what sets of real numbers/complex numbers/quaternions does Solèr’s theorem result in for the star division rings? In constructive mathematics, the notion of real numbers/complex numbers/quaternions bifurcates into many different incompatible sets depending upon the definition used to define the real numbers/complex numbers/quaternions.
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics?
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics? If so, what sets of real numbers/complex numbers/quaternions does Solèr’s theorem result in for the star division rings? In constructive mathematics, the notion of real numbers/complex numbers/quaternions bifurcates into many different incompatible sets depending upon the definition used to define the real numbers/complex numbers/quaternions.
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics? If so, what sets of real numbers/complex numbers/quaternions does Solèr’s theorem result in for the division rings? In constructive mathematics, the notion of real numbers/complex numbers/quaternions bifurcates into many different incompatible sets depending upon the definition used to define the real numbers/complex numbers/quaternions.
Solèr’s theorem says that for every star division ring $R$ and every $R$-module $H$ with a orthomodular hermitan form $\langle (-),(-) \rangle:H \times H \to R$ such that there exists an infinite orthonormal sequence $e:\mathbb{N} \to H$, $R$ is either one of the the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, or the quaternions $\mathbb{H}$, and $H$ is a Hilbert space over $R$. Assuming that the star division rings used are Heyting division rings (or else Solèr’s theorem is most likely false), is Solèr’s theorem true in constructive mathematics? If so, what sets of real numbers/complex numbers/quaternions does Solèr’s theorem result in for the star division rings? In constructive mathematics, the notion of real numbers/complex numbers/quaternions bifurcates into many different incompatible sets depending upon the definition used to define the real numbers/complex numbers/quaternions.